a) A k-out-of-n system is one that will function if and only if at least k...

a) A k-out-of-n system is one that will function if and only if at least k of the n individual components in the system function. If individual components function independently of one another, each with probability 0.8, what is the probability that a 4-out-of-6 system functions?

b) Obtain ?(?(?−2)) where ? ~???????(?)

c) Service calls arrive at a maintenance center according to a Poisson process, with average 3.1 calls per minute.

(i) Obtain the probability that no more than 4 calls arrive in a minute.

(ii) Obtain the probability that more than 7 calls arrive in a three-minute interval

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Engineering system of type k-out-of-n is operational if at least k out of n components are...

Engineering system of type k-out-of-n is operational if at least k out of n components are operational. Otherwise, the system fails. Suppose that a k-out-of-n system consists of n identical and independent elements for which the lifetime has Weibull distribution with parameters r and λ. More precisely, if T is a lifetime of a component, P(T ≥ t) = e−λtr, t ≥ 0. Time t is in units of months, and consequently, rate parameter λ is in units (month)−1. Parameter...

An engineering system consisting of n components is said to be a k-out-of-n system (k ≤...

An engineering system consisting of n components is said to be a k-out-of-n system (k ≤ n) if the system functions if and only if at least k of the n components function. Suppose that all components function independently of each other. (a) If the ith component functions with probability Pi , i=1, 2, 3, 4, compute the probability that a 2-out-of-4 system functions. (b) Repeat (a) for a 3-out-of-5 system.

The production function is f(K,N) = N/2 + √ K, where N is the amount of...

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Show that a graph with at least 2k vertices is k-connected if and only if for...

Show that a graph with at least 2k vertices is k-connected if and only if for any two unrelated subsets X, Y of V, such that | X | = k = | Y |, there are k foreign paths between X and Y.

Consider the following recurrence relation defined only for n = 2^k for integers k such that...

Consider the following recurrence relation defined only for n = 2^k for integers k such that k ≥ 1: T(2) = 7, and for n ≥ 4, T(n) = n + T(n / 2). Three students were working together in a study group and came up with this answer for this recurrence: T(n) = n * log2 (n) − n − log2 (n) + 8. Determine if this solution is correct by trying to prove it is correct by induction.

An economy has the production function Y=0.4(K+N). In the current period, K=100 and N=100. Graph the...

An economy has the production function Y=0.4(K+N). In the current period, K=100 and N=100. Graph the relationship between output and capital, holding labor constant at its current value. What is the MPK? Graph the relationship between output and labor, holding capital constant at its current value. Find the MPN for an increase of labor from 100 to 110. Compare this result with the MPN for an increase in labor from 200 to 210.

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a) A k-out-of-n system is one that will function if and only if at least k...

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